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Centuries from Australia A's Ben McDermott and Jack Wildermuth have thwarted India's push for victory on the final day of their pink-ball tour game in Sydney.

Ben McDermott and Jack Wildermuth celebrated centuries as India spearhead Mohammed Shami's confidence took a hit on Sunday night, when his bouncer barrage at the SCG proved costly and ineffectual.

McDermott and Wildermuth, who finished unbeaten on 107 and 111 respectively when the captains agreed to shake hands at 8.54pm AEDT, ensured Australia A finished 4-307 and salvaged a draw in the pink-ball tour game.

The visitors were well placed to win the match, having reduced the hosts to 3-25 after an overnight declaration set them a target of 473 on the final day.

Shami removed Marcus Harris and Joe Burns in Sunday's productive opening spell.

But he crashed back to earth in the night session, when Wildermuth and McDermott shared a boundary-laden partnership worth 165 runs.

Wildermuth cracked a ton from 109 deliveries in a tick over two hours, while McDermott eased to three figures in 161 balls.

Both batsmen were called into the Australia A squad on short notice after injuries to Will Pucovski and Mosies Henriques.

"I was really proud of how we fought back," Australia A captain Alex Carey said.

"I'm sure they will remember making a hundred against India for a very long time.

"They (Jasprit Bumrah and Shami) are some of the best Test bowlers in the world."

Wildermuth was peppered with short stuff by Shami and Bumrah.

The allrounder initially looked uncomfortable and could have easily been dismissed while hooking Shami as he approached his half-century.

But a diving Bumrah grassed the catch at fine leg, encouraging Wildermurth to smack two sixes during Shami's next over.

India claimed a sole wicket in Sunday's final two sessions, when Carey fell victim to Hanuma Vihari's part-time offspin after a steadying 58.

Shami finished with figures of 2-58 from 13 overs in the final innings of the tune-up, while Bumrah went wicketless.

It came after Australia A copped a withering spray from Allan Border, who lashed their lack of intent in the field on Saturday night.

"They were meandering around. Brown's cows ... just going through the motions," Border said on Fox Sports.

"They gave up.

"If Alex Carey is in line to be an Australian captain, he's got a lot of work to do.

"I would have sent out some pretty terse messages about 'lifting your expletive, expletive game otherwise you're out of there, I'm going to get the under-16s from the Mosman cricket club to come and do a better job in the field'."

A fired-up Border also queried the precautionary decision to withdraw Sean Abbott (tight calf) from the attack.

Carey suggested Australia A were trying and had a good attitude but he'd welcome the chance to sit down with Border and hear his feedback.

"I love talking to the greats in Australian cricket and picking their brains. He's one of Australia's best captains and players," the keeper said.